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Bipolar Junction Transistors (BJT)
ELEC-H402/CH6: BJT 1
Chapter 6
Outline
• Bipolar Junction transistors– Structure and modes of operation
– Current-voltage characteristics
– Biasing a BJT
– Small-signal models
– Single-stage amplifiers
• Conclusions
ELEC-H402/CH6: BJT 2
BJT structure
• BJT is a three-port structure
• Two types: NPN or PNP transistors
• Actual on-chip implementation:
ELEC-H402/CH6: BJT 3
Remember P and N semiconductors ?
BJT operation: Active mode
• EB depletion region narrowsElectrons are able to cross depletion region from E to B
Holes are able to cross depletion region from B to E
ELEC-H402/CH6: BJT 4
EB forward biased, BC reverse biased
BJT operation: Active mode
• Electron concentration highest at the edge of depletion region of base
– Similar to PN junction (see chapter 2): 𝑛𝑝 0 = 𝑛𝑝0𝑒𝑣𝐵𝐸/𝑉𝑇
– Electron concentration profile creates E-B current
– At collector side, electrons are swept through depletion region
ELEC-H402/CH6: BJT 5
Electron profile in the E-B regions
E-B current:
𝐼𝑛 = 𝐴𝐸𝑞𝐷𝑛𝑑𝑛𝑝 𝑥
𝑑𝑥
⇒ 𝐼𝑛 = 𝐴𝐸𝑞𝐷𝑛 −𝑛𝑝 0
𝑊
BJT operation: Active mode
• Diffusing electrons are swept through the depletion region
• The collector current 𝑖𝐶 = 𝐼𝑛• Using previous results:
𝑖𝐶 = 𝐼𝑆𝑒𝑣𝐵𝐸/𝑉𝑇
with 𝐼𝑆 = 𝐴𝐸𝑞𝐷𝑛𝑛𝑝0/𝑊
ELEC-H402/CH6: BJT 6
At the collector …
BJT operation: Active mode
• Composed of holes injected from base to emitter
Proportional to 𝑒𝑣𝐵𝐸/𝑉𝑇 : 𝑖𝐵1 =𝐴𝐸𝑞𝐷𝑝𝑛𝑖
2
𝑁𝐷𝐿𝑝𝑒𝑣𝐵𝐸/𝑉𝑇
• Also composed of electrons that recombine with holes in P-region Holes are resuplied by external circuit, also Proportional to 𝑒𝑣𝐵𝐸/𝑉𝑇 :
𝑖𝐵2 =1
2
𝐴𝐸𝑞𝑊𝑛𝑖2
𝜏𝐵𝑛𝐴𝑒𝑣𝐵𝐸/𝑉𝑇
ELEC-H402/CH6: BJT 7
The base current
BJT: Active mode
• 𝑖𝐶 = 𝐼𝑆𝑒𝑣𝐵𝐸/𝑉𝑇
• 𝑖𝐵 =𝐴𝐸𝑞𝐷𝑝𝑛𝑖
2
𝑁𝐷𝐿𝑝+
1
2
𝐴𝐸𝑞𝑊𝑛𝑖2
𝜏𝐵𝑛𝐴𝑒𝑣𝐵𝐸/𝑉𝑇 =
𝑖𝐶
𝛽
• 𝑖𝐸 = 𝑖𝐶 + 𝑖𝐵 =𝛽+1
𝛽𝑖𝐶 =
1
𝛼𝐹𝑖𝐶
ELEC-H402/CH6: BJT 8
Summary of all currents
BJT: saturation mode
• Active mode if BC junction is reverse biased
• To have a BC junction forward biased, negative 𝑣𝐶𝐵 is required
ELEC-H402/CH6: BJT 9
If 𝒗𝑪𝑩 is low, no current 𝒊𝑪
BJT: current-voltage characteristics
ELEC-H402/CH6: BJT 10
… for npn transistor
𝑖𝐶 = 𝐼𝑆𝑒𝑣𝐵𝐸/𝑉𝑇
𝑖𝐶 = 𝛼𝐹𝑖𝐸
𝑣𝐵𝐸 ≈ 0.7 𝑉
BJT: current-voltage characteristics
• For a given 𝑣𝐵𝐸, increasing 𝑣𝐶𝐸 increases the reverse-biasvoltage on collector-base junction increases width of depletion region
Decreases the effective base width
Increases 𝐼𝑆 = 𝐴𝐸 𝑞𝐷𝑛𝑛𝑝0/𝑊
increases 𝑖𝐶
ELEC-H402/CH6: BJT 11
Early effect
BJT: current-voltage characteristic
ELEC-H402/CH6: BJT 12
Large-signal equivalent circuit
𝑟𝑜 =𝑉𝐴𝐼𝐶′
𝐼𝐶′ = 𝐼𝑆𝑒
𝑉𝐵𝐸/𝑉𝑇
𝑖𝐶 = 𝐼𝑆𝑒𝑣𝐵𝐸/𝑉𝑇
𝑖𝐵 =𝑖𝐶𝛽
𝑖𝐸 = 𝑖𝐶 + 𝑖𝐵 = 𝛽 + 1 𝑖𝐵
𝑣𝐵𝐸 ≈ 0.7 𝑉
Biasing BJTs
• Fix 𝑉𝐵𝐸 so that small variations of 𝑣𝑏𝑒 result in linear change in 𝑖𝑐
• Also ok to fix 𝐼𝐶 or 𝐼𝐸
ELEC-H402/CH6: BJT 13
Why biasing?
Biasing BJTs
• Single power supply
• Poor performances against BJT dispersion
ELEC-H402/CH6: BJT 14
with discrete-circuit bias arrangement
𝑉𝐵𝐵 =𝑅2
𝑅1 + 𝑅2𝑉𝐶𝐶
𝑅𝐵 = 𝑅1||𝑅2
𝑉𝐵𝐵 = 𝑅𝐵𝐼𝐵 + 𝑉𝐵𝐸 + 𝑅𝐸𝐼𝐸
𝐼𝐵 =𝐼𝐸
𝛽 + 1
𝑉𝐵𝐸 ≈ 0.7 𝑉
⇒ 𝐼𝐸 =𝑉𝐵𝐵 − 𝑉𝐵𝐸
𝑅𝐸 +𝑅𝐵𝛽 + 1
Try to make robust against transistor
dispersion with 𝑉𝐵𝐵 ≫ 𝑉𝐵𝐸 and 𝑅𝐸 ≫𝑅𝐵
𝛽+1
Biasing BJTs
• Also poor performances against BJT dispersion
ELEC-H402/CH6: BJT 15
with two-power supply arrangement
⇒ 𝐼𝐸=𝑉𝐸𝐸 − 𝑉𝐵𝐸
𝑅𝐸 +𝑅𝐵𝛽 + 1
𝑅𝐵𝐼𝐵 + 𝑉𝐵𝐸 + 𝑅𝐸𝐼𝐸 = 𝑉𝐸𝐸
• Try to make robust against transistor dispersion
with 𝑉𝐸𝐸 ≫ 𝑉𝐵𝐸 and 𝑅𝐸 ≫𝑅𝐵
𝛽+1
• If base connected to ground, biasing almosttotally independent from 𝛽
Biasing BJTs
• Resistor 𝑅𝐵 provides negative feedback, which helps stabilizing bias point
ELEC-H402/CH6: BJT 16
with collector-to-base feedback resistor
𝑉𝐶𝐶 = 𝑅𝐶𝐼𝐶 + 𝑅𝐵𝐼𝐵 + 𝑉𝐵𝐸
𝑉𝐶𝐶 = 𝑅𝐶𝐼𝐶 + 𝑅𝐵𝐼𝐸
𝛽 + 1+ 𝑉𝐵𝐸
⇒ 𝐼𝐸=𝑉𝐶𝐶 − 𝑉𝐵𝐸
𝑅𝐶 +𝑅𝐵𝛽 + 1
Try to make robust against transistor
dispersion with 𝑉𝐶𝐶 ≫ 𝑉𝐵𝐸 and 𝑅𝐶 ≫𝑅𝐵
𝛽+1
Biasing BJTs
• Emitter current independent of transistor parameters ⇒ 𝐼𝐸= 𝐼
• Source current implemented with BJT current mirror
ELEC-H402/CH6: BJT 17
with a constant-current source
𝐼𝑅𝐸𝐹 =𝑉𝐶𝐶 − 𝑉𝐵𝐸 + 𝑉𝐸𝐸
𝑅
𝐼 = 𝐼𝑅𝐸𝐹
BJT small signal model
ELEC-H402/CH6: BJT 18
Small-signal operation: collector current
𝑖𝐶 = 𝐼𝐶𝑒𝑣𝑏𝑒/𝑉𝑇
⇒ 𝑖𝐶≈ 𝐼𝐶 1 +𝑣𝑏𝑒𝑉𝑇
⇒ 𝑖𝐶≈ 𝐼𝐶 +𝐼𝐶𝑉𝑇𝑣𝑏𝑒
⇒ 𝑖𝑐=𝐼𝐶𝑉𝑇𝑣𝑏𝑒
⇒ 𝑖𝑐= 𝑔𝑚𝑣𝑏𝑒 with 𝑔𝑚 = 𝐼𝐶/𝑉𝑇
BJT small signal model
ELEC-H402/CH6: BJT 19
base current and input resistance
𝑖𝐵 =𝑖𝐶𝛽=𝐼𝐶𝛽+1
𝛽
𝐼𝐶𝑉𝑇𝑣𝑏𝑒
𝑖𝐵 = 𝐼𝐵 + 𝑖𝑏
⇒ 𝑖𝑏 =1
𝛽
𝐼𝐶𝑉𝑇𝑣𝑏𝑒
⇒ 𝑖𝑏 =1
𝑟𝜋𝑣𝑏𝑒
with 𝑟𝜋 =𝛽𝑉𝑇
𝐼𝐶=
𝛽
𝑔𝑚=
𝑉𝑇
𝐼𝐵
BJT small signal model
• Voltage-controlled current source
• current-controlled current source
ELEC-H402/CH6: BJT 20
Hybrid 𝝅-model
𝑖𝑒 =𝑣𝑏𝑒𝑟𝜋
+ 𝑔𝑚𝑣𝑏𝑒 =𝑣𝑏𝑒𝑟𝜋
+ 𝑔𝑚 𝑟𝜋𝑖𝑏 =𝑣𝑏𝑒𝑟𝜋
+ 𝛽𝑖𝑏
𝑔𝑚 = 𝐼𝐶/𝑉𝑇 and 𝑟𝜋 =𝛽
𝑔𝑚=
𝑉𝑇
𝐼𝐵
BJT small signal model
ELEC-H402/CH6: BJT 21
… with output resistance 𝒓𝒐
𝑔𝑚 =𝐼𝐶𝑉𝑇
𝑟𝜋 =𝑉𝑇𝐼𝐵
= 𝛽𝑉𝑇𝐼𝐶
𝑟𝑜 =𝑉𝐴𝐼𝐶
BJT small signal model
ELEC-H402/CH6: BJT 22
T-model also exists
𝑔𝑚 =𝐼𝐶𝑉𝑇
𝑟𝑒 =𝑉𝑇𝐼𝐸= 𝛼
𝑉𝑇𝐼𝐶
𝑟𝑜 =𝑉𝐴𝐼𝐶
𝛼 =𝛽
𝛽 + 1𝛽 =
𝛼
1 − 𝛼
Common-emitter amplifier
ELEC-H402/CH6: BJT 23
Polarized with current source
𝐼𝐸 = 𝐼 𝐼𝐶 =𝛽
𝛽 + 1𝐼𝐸 =
𝛽
𝛽 + 1𝐼
𝐼𝐵 =1
𝛽𝐼𝐶 =
1
𝛽 + 1𝐼
BJT withparameters 𝛽, 𝑉𝑇 and 𝑉𝐴
Common-emitter amplifier
ELEC-H402/CH6: BJT 24
Small-signal equivalent
𝑅𝑖𝑛 = 𝑅𝐵||𝑟𝜋
Gain, input resistance, output resistance ?
𝑣𝜋 = 𝑣𝑖
𝑣𝑜 = −𝑔𝑚𝑣𝜋 𝑟𝑜 𝑅𝐶 𝑅𝐿 = −𝑔𝑚𝑣𝑖 𝑟𝑜 𝑅𝐶 𝑅𝐿
⇒ 𝐴𝑣 =𝑣𝑜𝑣𝑖= −𝑔𝑚 𝑟𝑜 𝑅𝐶 𝑅𝐿
𝑅𝑜𝑢𝑡 = 𝑅𝐶||𝑟𝑜
CB and CC amplifier
ELEC-H402/CH6: BJT 25
Find 𝑨𝒗, 𝑹𝒊𝒏 and 𝑹𝒐𝒖𝒕 as exercice
Gain close to 1 => buffering stage
Same gain as CE, but non-inverting
BJT vs MOSFET
• Small input capacitance => very high speed (good for RF !)
• Higher transconductance => higher gain
• BJT amplifiers more linear than MOSFET amplifier stages
• BJT have lower output impedances and can handle higheroutput currents
• More choices for discrete components
ELEC-H402/CH6: BJT 26
BJT advantages
BJT vs MOSFET
• BJT are current-operated (rather than voltage operated)
Higher consumption
• Lower input resistance than MOSFET
• BJTs are harder to scale to large quantities
• BJTs have more fabrication dispersion
More difficult to make good mirror currents, differentialpairs, etc.
• Physical size about 10x as large as MOSFET
ELEC-H402/CH6: BJT 27
BJT drawbacks
BJT vs MOSFET
• MOSFET are easy to scale– Double the current? Double the width!
• High input impedance (almost infinite at low frequencies)
• Output are controlled by input voltage (not current)
Much lower power consumption
Main advantage MOSFET won for chip manufacturing
• Easy to make indentical MOSFETs– Good for CMOS transistors, mirror currents, differential pairs, etc.
• Mostly for integrated circuits, not discrete circuits
• Size about 10x smaller than BJT
ELEC-H402/CH6: BJT 28
MOSFET advantages
BJT vs MOSFET
• Input capacitance
Not good for high frequencies
• Higher output resistance than BJT
Not suited to drive low-impedance load
• Lower gain per stage
Amplifier stages need to be cascaded
Each stage adds noise
SNR degrades
ELEC-H402/CH6: BJT 29
MOSFET drawbacks